Question: Rewrite as a simplified fraction. ${2.27\overline{4} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2274.4444...\\ 100x &= 227.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2047}$ ${x = \dfrac{2047}{900}} \text{or} {2 \dfrac{247}{900}}$